Bibliographic Information

K-theory

M.F. Atiyah ; notes by D.W. Anderson

(Advanced book classics)

Addison-Wesley, Advanced Book Program, c1989

  • : pbk.

Available at  / 52 libraries

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Note

Reprint. Originally published: New York : W.A. Benjamin, 1967

Includes bibliographical references

Contents of Works

  • K-thoery
  • Power operations in K-theory
  • K-thoery and reality

Description and Table of Contents

Description

These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory.The theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism. In addition to the lecture notes proper, two papers of mine published since 1964 have been reproduced at the end. The first, dealing with operations, is a natural supplement to the material in Chapter III. It provides an alternative approach to operations which is less slick but more fundamental than the Grothendieck method of Chapter III, and it relates operations and filtration. Actually, the lectures deal with compact spaces, not cell-complexes, and so the skeleton-filtration does not figure in the notes. The second paper provides a new approach to K-theory and so fills an obvious gap in the lecture notes.

Table of Contents

Vector Bundles * Basic definitions * Operations on vector bundles * Sub-bundles and quotient bundles * Vector bundles on compact spaces * Additional structures * G-bundles over G-spaces K-Theory * Definitions * Elementary properties * The Bott periodicity theorem * Kg(X) * Computations of K*(X) for some X * Multiplication in K*(X,Y) * The Thom isomorphism Operations * Exterior powers * The Adams operations * The group J(X) * Reprint: Power operations in K-Theory * Reprint: K-Theory and reality

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Details

  • NCID
    BA07465742
  • ISBN
    • 0201093944
    • 0201407922
  • LCCN
    88022327
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Redwood City, Calif. ; Tokyo
  • Pages/Volumes
    xviii, 166, [50] p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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